8 slope

ISSN: 2319-8753
International Journal of Innovative Research in
Science, Engineering and Technology
(An ISO 3297: 2007 Certified Organization)
Vol. 2, Issue 12, December 2013
Copyright to IJIRSET www.ijirset.com 7114
Slope Stability Analysis under Rapid rawdown
Cndition and Siesmic Loads of Earth Dam
(Case Study: Mandali Dam)
Prof. Dr. Saleh I. Khassaf1
, Dr. Maha Rasheed Abdoul- Hameed 2
, Nabaa Noori Shams Al-deen3
Professor, Civil Dept, College of Engineering/ university of Kufa, / Najaf, Iraq1
Doctor, Civil Dept, Ministry of water Resources / Baghdad, Iraq 2
Engineering, Civil Dept, College of Engineering / university of Kufa, / Najaf, Iraq 3
Abstract: The one of the most dangerous conditions of earth dams for the upstream side slope is rapid drawdown
condition when the countervailing upstream water pressure has disappeared, it causes a danger to the upstream slope. In
this work, by applying the Morgenstern-Price presented by the computer program SLIDE V.6.0 is applied to define the
potential slip surface and calculate the factor of safety of zoned earth dams (Mandali dam in Iraq) under rapid
drawdown condition for maximum elevation with seismic forces effects. It founded that the stability of the upstream
slope of Mandali dam is dramatically decreased but still in stable during rapid drawdown condition.
Keywords: Earth Dam, The finite element, Morgenstern-Price method, factor of safety, Seismic force, side slope
stability, paid drawdown
I. INTRODUCTION
Stability analysis during rapid drawdown is an important consideration in the design of embankment dams. During
rapid drawdown, the stabilizing effect of the water on the upstream face is lost, but the pore-water pressures within the
embankment may remain high. As a result, the stability of the upstream face of the dam can be much reduced. The
dissipation of pore-water pressure in the embankment is largely influenced by the permeability and the storage
characteristic of the embankment materials. Highly permeable materials drain quickly during rapid drawdown, but low
permeability materials take a long time to drain.
In order to lower the phreatic line and pore water pressure as well as the hydrodynamic pressure in the upstream shell,
drains in the upstream slope’s base and at the intermediate level should be installed, if appropriate. These upstream
drains are capable of draining the upstream slope and making the equipotential lines tend to become horizontal. They
have a very significant effect on the stability of the upstream slope during drawdown [Tran, 2008].
Traditional limit equilibrium methods will be utilized in the slope stability analysis and the accommodation of saturated
and unsaturated pore-water pressures will be considered (Fredlund and Feng (2011))
In this study, a finite element software, SLIDE V.6.0 computer program , is used to determine phreatic line and factor
of safety. SLIDE is2D limit equilibrium slope stability program for evaluating the safety factor or probability of failure,
of circular or non-circular failure surfaces in soil or rock slopes. Slide analyzes the stability of slip surfaces using
vertical slice limit equilibrium methods although the Slide groundwater analysis is geared towards the calculation of
pore pressures for slope stability problems
The drawdown is known as one of the most dangerous conditions for the upstream side slope. When the countervailing
upstream water pressure has disappeared, it causes a danger to the upstream slope. The upstream shell cannot stay
stabile under the hydrodynamic pressure due to rapid drawdown. Soils inside the dam body remain saturated and
seepage commences from it towards the upstream slope. Seepage and hydrodynamic pressures create downward forces
acting on the upstream slope. Those are adverse to the stability and create a critical condition to the upstream slope.
The Rapid Drawdown Condition occurs when a slope that is used to retain water experiences a rapid (sudden) lowering
of the water level and the internal pore pressures in the slope cannot reduce fast enough.

ISSN: 2319-8753
Excess pore pressure refers to changes in pore pressure within a soil due to rapidly drawdown of pounded water
in upstream side conditions (undrained loading). Materials with low permeability such as clays, may exhibit this
behavior. With the so-called "B-bar" method, the change in pore pressure is assumed to be directly proportional to the
change in vertical stress. The excess pore pressure is given by :
∆u = B
_
∆V . . . . . . . . . . . (1)
Where:
∆u = excess pore water pressure caused by drawdown condition.
B
_
= (B-bar) overall pore pressure coefficient for earth fill material.
∆V = change in vertical effective stress.
From equation (1), it can be noting that the value of the excess pore pressure is dependent on the value of (B-bar)
coefficient. The value of (B-bar) coefficient is dependent on the type of soil and properties of soil. If (B-bar) coefficient
is defined about 0, the soil is free to drain and no excess pore water pressure is developed in upstream side. If (B-bar)
coefficient is defined about 1, the undrained condition is applied and excess pore pressure is developed in upstream
side. The value of (B-bar) coefficient close to 1 represents critical condition of rapid drawdown in upstream side and
should be selected to any soils which have low permeability
II. MORGENSTERN AND PRICE’S METHOD
The the Morgenstern-Price method was developed by Morgenstern and Price (1965), which considers not only the
normal and tangential equilibrium but also the moment equilibrium for each slice in circular and non-circular slip
surfaces. In this method, a simplifying assumption is made regarding the relationship between the interslice shear
forces (X) and the interslice normal forces (E) as:
Xf(x)E
……… (2)
where, f(x) is an assumed function that varies continuously across the slip, and (λ) is an unknown scaling factor that is
solved for as part of the unknowns.
The unknowns that are solved for in the Morgenstern and Price method are the factor of safety (FOS), the scaling
factor (), the normal forces on the base of the slice (P), the horizontal interslice force (E), and the location of the
interslice forces (line of thrust). Once the above unknowns are calculated using the equilibrium equations, the vertical
component of the resultant force on the interslice forces (X) is calculated from equation (2).
 
m
cXX ull
f
W LR
P

  









 


sintansin
1
. . . . . . . . . . . (3)
where:
P: Normal force on the base of the slice
W: Weight of slice
XR : Vertical component of the resultant force on the interslice (from right side of slice)
XL : Vertical component of the resultant force on the interslice (from left side of slice)
Two factor of safety equations are computed, one with respect to moment equilibrium (Fm) and the other with
respect to force equilibrium (Ff). The moment equilibrium equation is taken with respect to a common point as:
   
 





P
c
F
f
m
Wd
RulPl tan
. . . . . . . . . . . . . . (4)
For circular slip surfaces: ƒ = 0, d = Rsinα and R = constant;
  







sin
tan
W
ulPlc
Fm
. . . . . . . .. . . . .. (5)

ISSN: 2319-8753
The factor of safety with respect to force equilibrium is:
  







sin
costan
P
ulPlc
F f
. . . . . . . . . . . . (6)
On the first iteration, the vertical shear forces ( XR and XL ) are set to zero. On subsequent iterations, the
horizontal interslice forces are first computed from:
      costan
1
sin

 ulPlc
f
PELER
. . . . . . . . . . . . (7)
where:
ER: Horizontal interslice force (from right side of slice)
EL: Horizontal interslice force (from left side of slice)
l: The inclined width of slice
u: Pore water pressure
P: Normal force on the base of the slice
This method of slope stability analysis, which is valid for slip surfaces of any arbitrary shape, is considered as the
more general rigorous method [Baker, 1980]. It stems its generality from the fact that no stringent restriction is imposed
neither on the direction or location of the interslice forces nor on the shape of the slip surface analyzed [Al-Jorany,
1996].
Seismic activity is associated with complex oscillating patterns of accelerations and ground motions, which generate
transient dynamic loads due to the inertia of the dam and the retained body of water. Horizontal and vertical
accelerations are not equal, the former being of greater intensity. For design purposes both should be considered
operative in the sense least favourable to stability of the dam. Horizontal accelerations are therefore assumed to operate
normal to the axis of the dam.(Novak and Nalluri,(2007))
If seismic coefficients are defined, a seismic force will be applied to each slice as follows:
Seismic Force = Seismic Coefficient * Slice Weight . . . . . . . (8)
From this definition it can be observed that the seismic force increases when slice weight increases.
III.CASE STUDY
The Mandali Dam is one of an earth fill dams in Iraq, which had been designed by Directorate General of Dam and
Reservoirs. Which is located on Harran Wadi, in the governorate of Diyala which is extends to the northeast of
Baghdad. The dam site is situated upstream Koma sang pipe line headwork.the area of the dam is bounded by the
following coordinates (373700-378500) N, (554500-565000) E. The dam is a low dam, which acts in most of its parts
as a submerged weir. The Wadi bed is gravely and permeable to some depth as it is clear from geological investigation
Mandali dam with a central core total length of the dam is about (1316 m) and its maximum height is about (14m). The
shell, which is composed mainly of poorly graded gravel with high percentage of coarse gravel , and the central core,
the investigation and laboratory testing show clay the available materials at site as a construction material for core
(Directorate General of Dams and Reservoire,(2004)).
The finite element mesh used in this analysis is as shown in figure (1); 3 node triangles elements are used to describe
the domains. The mesh contains 2500 element and 1624 node; The first step in our analysis are concerning about
selected the numbers of element and selected these value when the number of element became independents of solution,
in this case any increment in the number of element dose not effected on the values of solution in domain of analysis
the number of elements is selected from mesh generation from change in phreatic surface

ISSN: 2319-8753
(b)
(a)
Fig.1 Mandali dam (a) typical cross section of Mandali dam (b) Finite Element Mesh for the Mandali Dam
IV.ANALYSIS AND DISCUSSION
V.
Fig. 2. The most critical slip surface (a) For steady state condition, before drawdown, FOS = 2.983 (b) For rapid drawdown condition from EL. 182.5
m to EL. 172.0 m, FOS = 1.837 (c) For rapid drawdown condition with seismic load effect (0.07) in one directions, FOS = 1.376 (d) for rapid
drawdown condition with seismic load effect (0.07) in two directions, FOS = 1.254
The slope stability against landslide risk is represented by safety factor (SOF), which is determined using
Morgenstern-Price Method. The slope stability in the rapid drawdown was examined. In a rapid drawdown of water
level, deformation and crack occurred in the dam model at the upstream slope. The failure process in the rapid
drawdown of water level was begun with movement of soil particles in the surface of upstream slope model.
Above figure (2) shows, (a) the value and location of most critical slip surface for steady state condition (before
drawdown). (b) the value and location of most critical slip surface for rapid drawdown condition from EL. 182.5 m to
EL. 172.0 m. (c) and (d) show the value and location of most critical slip surface for rapid drawdown condition with
(a) (b)
(c) (d)

ISSN: 2319-8753
seismic load(0.07g) effect for one and two direction. It show that the value of factor of safety of upstream decrease
when rapid drawdown condition and seismic load effect
VI. CONCLUSION
In this study, a finite element software, SLIDE V.6.0 is used to determine the factor of safety under rapid
drawdown condition from EL. 182.5 m to EL. 172.0 m and rapid drawdown condition with seismic load (0.07g) effect
for one and two direction. It is found that the factor of safety of upstream decrease when rapid drawdown condition and
seismic load effect and the upstream slope is still stable during rapid drawdown, and the minimum value obtained for
FOS is about 1.254 during rapid drawdown and seismic load coefficient 0.07.
REFERENCES
[1] Al-Jorany, A.N., (1996), “Slope Stability Analysis”, Ph.D. Dissertation, Department of Civil Engineering, University of Baghdad
[2] Baker R., (1980). “Determination of the Critical Slip Surface in Slope Stability Computations”, International Journal for Numerical and
Analytical Methods in Geomechanics, Vol.4.
[3] Directorate General of Dams and Reservoirs, (2004) “ Mandali Dam Project- Geological Report” Ministry of water Resources
[4] Fredlund Murray and Feng Tiequn, (2011), “Combined Seepage and Slope Stability Analysis of Rapid Drawdown Scenarios for Levees
Design”, Soil Vision System Ltd, Saskatoon, 640 Broadway Ave, Suite 202, 57N, SK,Canada
[5] Novak P.A. Moffat and Nalluri C., (2007) “Hydraulic Structures”, School of Civil Engineering and Geosciences University Upon Tyne, UK
and Formerly Department of Civil and Structural Engineering, UMIST, University of Manchester, UK (Fourth Edition)
[6] Tran X. Tho, (2008) “Stability Problems of an Earth Fill Dam in Rapid Drawdown Condition ”, Grant Project, No.1/9066/02
[7] U.S. Army Crops of Engineers, (2003a), “Slope Stability”, Manual, EM1110-2-1902, Chapter 2.; Design Considerations

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